Ph.D Thesis

Ph.D StudentSzafranek Dana
SubjectSource-Model Technique for Computations of Scattering by,
and Waveguiding across, Arrays of Cylinders
Embedded in Layered Media
DepartmentDepartment of Electrical and Computer Engineering
Supervisor PROFESSOR EMERITUS Yehuda Leviatan
Full Thesis textFull thesis text - English Version


Electromagnetic (EM) scattering by and wave-guiding across arrays of cylinders has been studied for decades. The motivation lies in many different applications that incorporate arrays of 2D-like objects, such as wires, strips, or rods. Mature applications include frequency selective surfaces, absorbing structures and polarizers which operate in the microwave and radio frequency range. In more recent applications, arrays of nanometer-scale cylinders have been used in the optical regime as frequency selective surfaces, reflection or transmission gratings, biological and chemical sensors, and are still considered as potential elements in nanometer-scale integrated optical circuits.

This work presents a computational technique for analysis of electromagnetic scattering by, and waveguiding across, arrays of penetrable cylinders with arbitrary, smooth cross-sections, against a multilayered background. The cylinders may be partially buried in a supporting penetrable substrate layer, or entirely buried in a multilayered structure. The solution scheme we suggest is a rigorous full-wave frequency-domain method based on the Source-Model Technique. For parametric studies of the eigenmodes we suggest an efficient mode-tracking algorithm that is based on the physical perturbation theory, and is devoid of spurious solutions. Our method is general, robust, computationally efficient, and yields credible results.

Special attention is given to the analysis of arrays of partially buried cylinders between two background media. This type of anchoring of the arrays of cylinders into a background layer may be a side-effect of the fabrication process, or a desirable feature that increases the mechanical robustness in certain applications. Previous works demonstrate that near such an intersection of the cylinder with a planar interface separating two background media, the fields change rapidly like they would near a corner, because of the sharp meeting point of three media there. The analytical behavior of the fields can be found at the quasi-static limit for some composites, e.g., a composite of three dielectric materials, yet it is difficult to provide a convergent analytical formulation in the general electrodynamic case. We suggest a novel algorithm for numerically treating these three-media intersections. Our method allows for intricate modeling of rapid spatial-variations of the fields there, and thus provides a numerical remedy for the field divergence problem at the intersection.

We show representative examples for cylinders with circular and triangle-like cross sections, for lossy and lossless structures, at wavelength or deep sub-wavelength scale. We also demonstrate some linear EM phenomena related to surface-plasmon-polariton type waves. Our method enables the calculation and demonstration of yet-unseen dynamics of physical values as a function of the relative depth of burial of the array in the layered background, such as the scattered energy, or the modal wave number and mode profile of an un-excited structure. We demonstrate the importance of careful geometrical modeling and full-wave simulations of the array and background media, which have been made possible with our technique.